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Proof sin(10) is irrational.

  1. Oct 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove [itex] \sin{10} [/itex], in degrees, is irrational.


    2. Relevant equations
    None, got the problem as is.


    3. The attempt at a solution
    Im kinda lost.
     
  2. jcsd
  3. Oct 15, 2012 #2

    Zondrina

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    Okay, are you familiar with proof by contradiction?

    Start by contradicting the statement :

    Suppose that sin(10) is irrational.
     
  4. Oct 15, 2012 #3

    Dick

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    Let x=sin(10). You'll want to find a polynomial x satisfies and show it has no rational root. Hint: sin(30)=1/2=sin(10+10+10).
     
  5. Oct 15, 2012 #4
    I should suppose sin(10) is rational, if i am to contradict the statement, shouldnt i?
     
  6. Oct 15, 2012 #5

    jedishrfu

    Staff: Mentor

    yes and that means that sin(10) can be represented by the ratio of two integers a and b sin(10) = a/b

    next step...
     
  7. Oct 15, 2012 #6

    Dick

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    Zondrina's hint contains nothing of any real substance to start solving the problem. Mine does. I suggest you start trying it.
     
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